# A Coyote and a Rat#

A coyote notices a rat running past it, toward a bush where the rat will be safe. The rat is running with a constant velocity of $$v\_{\text{rat}} = {{ params.v_r }} \rm{m/s}$$ and the coyote is at rest, $$\Delta x = {{ params.d_x }} \rm{m}$$ to the left of the rat. However, at $$t=0 \rm{s}$$, the coyote begins running to the right, in pursuit of the rat, with an acceleration of $$a\_{\text{coyote}} = {{ params.a_c }} \rm{m/s^2}$$.

Set your reference frame to be located with the origin at the original location of the coyote and the rightward direction corresponding to the positive $$x$$-direction.

## Part 1#

Write the position of the coyote as a function of time $$x\_{\text{coyote}}(t)$$. Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

$$t$$

t

$$\Delta x$$

dx

$$v\_{\text{rat}}$$

vr

$$a\_{\text{coyote}}$$

ac

## Part 2#

Write the velocity of the coyote as a function of time $$v\_{\text{coyote}}(t)$$. Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

$$t$$

t

$$\Delta x$$

dx

$$v\_{\text{rat}}$$

vr

$$a\_{\text{coyote}}$$

ac

## Part 3#

Write the position of the rat as a function of time $$x\_{\text{rat}}(t)$$. Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

$$t$$

t

$$\Delta x$$

dx

$$v\_{\text{rat}}$$

vr

$$a\_{\text{coyote}}$$

ac

## Part 4#

Write the velocity of the rat as a function of time $$v\_{\text{rat}}(t)$$. Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

$$t$$

t

$$\Delta x$$

dx

$$v\_{\text{rat}}$$

vr

$$a\_{\text{coyote}}$$

ac

## Part 5#

At what time does the coyote catch the rat $$t\_{\text{catch}}$$?

Please enter in a numeric value in $$\rm{s}$$.

## Part 6#

At this time, what is the velocity of the coyote $$v\_{\text{coyote}}(t\_{\text{catch}})$$?

Please enter in a numeric value in $$\rm{m/s}$$.

## Part 7#

At this time, what is the velocity of the rat $$v\_{\text{rat}}(t\_{\text{catch}})$$?

Please enter in a numeric value in $$\rm{m/s}$$.

## Part 8#

What is the location at which the coyote will catch the rat $$x\_{\text{coyote}}(t\_{\text{catch}}) = x\_{\text{rat}}(t\_{\text{catch}})$$?

Please enter in a numeric value in $$\rm{m}$$.